IX. The eighteenth Centnty. 185
problems arc here translated' as specimens of the work of Japanese mathematicians at the close of the eighteenth century. "There is a circle in which a triangle and three circles, A, B, C, are inscribed in the manner shown in the figure.
Given the diameters of the three inscribed circles, required the diameter of the circumscribed circle." The rule given may be abbreviated as follows:
Let the respective diameters be xt y, and s, and let xy<*=a.
Then from «* take I (x — y}&\ • Divide a by this remainder and call the result b. Then from (A'+y)g take a, and divide 0.5 by this remainder and add b, and then multiply by s and by a. The result is the diameter of the circumscribed circle.1 To this rule is appended, with some note of pride, the words: "Feudal District of Kakegawa in Ycnshu Province, third month of 1795, Miyajima Sonobei Keichi, pupil of Fujitti Sadasuke of the School of Scki."
Another problem is stated as follows: "Two circles are described, one inscribing and the other circumscribing a quadri-
' From the edition of 1796. * That is